Ronald Koeman’s team suffered an early shock when Adam Idah’s penalty put Ireland ahead in Dublin in their Group B game.
But Liverpool’s Cody Gakpo netted a penalty soon after and the visitors wrapped up the points thanks to Weghorst’s second half strike.
Currently on loan at German side Hoffenheim from Premier League club Burnley, the towering Weghorst’s introduction at the interval proved a masterstroke by Koeman.
Weghorst had scored in the victory against Greece on Thursday and he showed no signs of sulking despite being initially left on the bench at the Aviva Stadium.
A third win from their four Group B matches lifted the Netherlands into second place, six points behind leaders France with a game in hand.
The top two will qualify for next year’s European Championship in Germany and Koeman’s men are in control of their own destiny.
They have a game in hand on third placed Greece, who are level on points with the Dutch, and sit six points ahead of Ireland.
Beaten in four of their five matches, Stephen Kenny’s hosts look certain to miss out on a place at the Euros.
After failed bids to reach the Euros two years ago and last year’s World Cup, it is shaping up to be another grim qualification campaign for the Irish.
Ireland’s defeat against France on Thursday had put them in trouble in the group, leaving fans hoping for a repeat of their famous victory over Holland in their last competitive meeting 22 years ago.
Desperately needing a fast start to put the Netherlands under pressure, the Republic got exactly that in the fourth minute.
Virgil van Dijk was penalised for handball as he challenged to clear James McClean’s corner.
The Liverpool captain complained but referee Irfan Peljto ignored his protests as Norwich striker Idah fired home from the spot.
It was the latest controversial moment involving Van Dijk, who was sent off for a foul on Newcastle’s Alexander Isak recently and earned an extra game suspension for his angry reaction to the decision.
Van Dijk’s blushes were spared by his Liverpool team-mate Gakpo in the 19th minute.
Ireland keeper Gavin Bazunu tripped Dutch defender Denzel Dumfries and Gakpo held his nerve to convert the penalty for his second goal in his last two games.
With the Netherlands revived after their sloppy start, the visitors went close when Donyell Malen’s low shot was saved by Bazunu.
Malen was denied again just before half-time, slipping through the Irish defence only for Bazunu’s stop to rescue his side.
Koeman’s side were well on top and they took the lead thanks to half-time substitute Weghorst in the 56th minute.
Frenkie De Jong found Dumfries with a lofted pass and when he turned the ball across goal, former Manchester United loanee Weghorst was perfectly placed to slot home.
AFP